Antiparticles as particles: QED${}_{2+1}$ and composite Fermions at $\nu =\frac{1}{2}$

Abstract

We present a continuum operator map that inverts the role of particles and antiparticles in three dimensional QED. This is accomplished by the attachment of specific holomorphic Wilson lines to Dirac fermions. We show that this nonlocal map provides a continuum realization of Son's composite fermions at $\nu =\frac{1}{2}$. The inversion of Landau levels and the Dirac-cone--composite-Fermion duality is explicitly demonstrated for the case of slowly varying magnetic fields. The role of Maxwell-terms as well as the connection of this construction to a gauge-invariant formulation of 3D gauge theories is also elaborated upon.

5+3 pages. 1 Figure

References in corpus (2)

• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Dirac fermion duality and the parity anomaly

Cited by in corpus (4)

• Fermionic dualities with axial gauge fields
• Scaling and Diffusion of Dirac Composite Fermions
• Dirac Equation Solution with Generalized tanh-Shaped Hyperbolic Potential: Application to Charmonium and Bottomonium Mass Spectra
• Holomorphicity, Vortex Attachment, Gauge Invariance and the Fractional Quantum Hall Effect